Semi-classical Schrodinger equations with harmonic potential and nonlinear perturbation
Language
en
Article de revue
This item was published in
Annales I.H.P., Analyse non linéaire. 2003, vol. 20, p. no. 3, 501-542
English Abstract
Solutions of semi-classical Schrodinger equation with isotropic harmonic potential focus periodically in time. We study the perturbation of this equation by a nonlinear term. If the scaling of this perturbation is critical, ...Read more >
Solutions of semi-classical Schrodinger equation with isotropic harmonic potential focus periodically in time. We study the perturbation of this equation by a nonlinear term. If the scaling of this perturbation is critical, each focus crossing is described by a nonlinear scattering operator, which is therefore iterated as many times as the solution passes through a focus. The study of this nonlinear problem is made possible by the introduction of two operators well adapted to Schrodinger equations with harmonic potential, and by suitable Strichartz inequalities.Read less <
English Keywords
Harmonic oscillator
nonlinear Schrodinger equation
scattering theory
Maslov index
Origin
Hal imported